Floating memristor emulator

ABSTRACT

The floating memristor emulator is based on a circuit implementation that uses grounded capacitors and CFOAs in addition to combinations of diodes and resistors to provide the required nonlinearity and time constants. This circuit results in low power consumption, cost reduction and ease of implementation because it avoids the use of multipliers, ADCs and RDACs. The present circuit is used in an FM demodulator, which exploits the frequency-dependence of the memristance. Successful use in the FM demodulator confirmed the functionality of the present floating memristor emulator circuit.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to memristors, and particularly to afloating memristor emulator that can be used in frequency-to-voltageconversion.

2. Description of the Related Art

Since its inception, several emulators have been presented for thegrounded memristor. However, only few floating memristor emulators areavailable in the literature. Those few designs have numerous components,which present size and power consumption problems.

Thus, a floating memristor emulator solving the aforementioned problemsis desired.

SUMMARY OF THE INVENTION

The floating memristor emulator is based on a circuit implementationthat uses grounded capacitors and CFOAs in addition to combinations ofdiodes and resistors to provide the required nonlinearity and timeconstants. This circuit results in low power consumption, cost reductionand ease of implementation because it avoids the use of multipliers,ADCs and RDACs. The present circuit may be used in an FM demodulator,which exploits the frequency-dependence of the memristance. Successfuluse in the FM demodulator confirmed the functionality of the presentfloating memristor emulator circuit.

These and other features of the present invention will become readilyapparent upon further review of the following specification anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a floating memristor emulator accordingto the present invention.

FIG. 2A is a schematic diagram showing an I_(M) model in terms of inputcurrent for a floating memristor emulator according to the presentinvention.

FIG. 2B is a schematic diagram showing an I_(R) model in terms ofemulator current for a floating memristor emulator according to thepresent invention.

FIG. 3A is a plot showing current and voltage waveform characteristicsof the floating memristor emulator according to the present invention.

FIG. 3B is a plot showing current-voltage characteristics with a widedifference in the resistance values of the floating memristor emulatoraccording to the present invention.

FIG. 4A is a plot showing current and voltage waveform characteristicsof the floating memristor emulator according to the present invention at2.9 kHz.

FIG. 4B is a plot showing current-voltage characteristics with narrowdifference in resistance values at 2.9 kHz of the floating memristoremulator according to the present invention.

FIG. 5 is a plot showing behavior at 6.0 kHz of the floating memristoremulator according to the present invention.

FIG. 6 is a schematic diagram showing a test circuit for the floatingmemristor emulator according to the present invention.

FIG. 7 is a schematic diagram showing a FM demodulator using thefloating memristor emulator according to the present invention.

FIG. 8 is a plot showing FM and the converted AM of the FM demodulatorusing the floating memristor emulator according to the presentinvention.

FIG. 9 is a plot showing the converted AM signal and the outputdemodulated signal of the FM demodulator using the floating memristoremulator according to the present invention.

FIG. 10 is a plot showing the input FM signal and the output modulatingsignal at the output of the low pass filter connected to the FMdemodulator using the floating memristor emulator according to thepresent invention.

Similar reference characters denote corresponding features consistentlythroughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present floating memristor emulator circuit includes four currentfeedback operational amplifiers (CFOA's 102 a, 102 b, 102 c, and 102 d),configured as shown in FIG. 1. The first 102 a, second 102 c, third 102b, and fourth 102 d current feedback operational amplifiers (CFOAs),each have y, x, z, and w terminals. The y terminal of first CFOA1 102 ais connected two the z terminal of the second CFOA2 102 c. The yterminal of the third CFOA3 102 b is connected to the z terminal of thefourth CFOA4 102 d. A differential voltage input, v_(inp), v_(inn) isformed from the y terminals of the first and third CFOAs (102 a, 102 b).The x terminals of CFOA1 102 a and CFOA3 102 b are in operablecommunication with each other. For example, a potentiometer R₁ may beconnected between the x terminals of CFOA1 102 a and CFOA3 102 b (thewiper portion being connected to CFOA3 102 b). Grounded capacitors C₁through C₄ are connected to their respective CFOAs (102 a, 102 c, 102 b,and 102 d). A parallel combination (R₃ and D₁) has a cathode portion ofD) connected to the w terminal of COFA1 102 a. The R₃, D₁ combination isconnected in series with the upper part of the potentiometer R₅ which isconnected to the y terminal of CFOA4 102 d. The wiper portion ofpotentiometer R₅ is connected to ground. A parallel combination (R₂ andD₂) has an anode portion of D₂ connected to the w terminal of COFA3 102b. The R₂, D₂ combination is connected in series with the lower part ofthe potentiometer R₅, which is connected to they terminal of CFOA2 102c. The input voltage produces a current through the resistance R₁ givenby:i _(R) ₁ =(v _(inp) −v _(inn) /R ₁.  (1)

This current will flow outward from terminal x of CFOA1 (102 a) andinward into terminal x of CFOA3 102 b. This current will be induced interminal z of CFOA1 (102 a), where it will be integrated by thecapacitor C₁ to produce a voltage given by:

$\begin{matrix}{v_{R_{p}} = {\frac{1}{C_{1}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{\mathbb{d}t}.}}}}} & (2)\end{matrix}$

This voltage will be induced on terminal w of CFOA1 (102 a) and willproduce an outward current from terminal w of CFOA1 (102 a), i_(Rp)through the parallel combination of R₃ and D₁ in series with the upperpart of the potentiometer R₅. This current can be expressed as:

$\begin{matrix}{i_{R_{p}} = {\frac{v_{R_{p}}}{R_{5{upper}} + R_{{eq}\; 1}}.}} & (3)\end{matrix}$

In equation (3), R_(5upper) is the resistance of the upper part of thepotentiometer R₅ and R_(eq1) is a nonlinear resistance that depends onthe status of the diode D₁. The voltage at terminal y of the CFOA 4 (102d) will depend on the status of the diode D₁. This voltage can beexpressed as:

$\begin{matrix}{v_{1} = {\frac{v_{R_{p}}\mspace{14mu} R_{5{upper}}}{R_{5{upper}} + R_{{eq}\; 1}}.}} & (4)\end{matrix}$

The voltage v₁ will be induced on terminal x of the CFOA4 (102 d) andwill be differentiated by the capacitor C₄. Thus, the outward current inthe lower input terminal will be given by:

$\begin{matrix}{i_{inn} = {C_{4}{\frac{\mathbb{d}v_{1}}{\mathbb{d}t}.}}} & (5)\end{matrix}$

In a similar way the current i_(R) ₁ will be induced in the terminal zof CFOA3 (102 b) and will be integrated by the capacitor C₃ to produce avoltage given by:

$\begin{matrix}{v_{R_{n}} = {\frac{- 1}{C_{3}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{\mathbb{d}t}.}}}}} & (6)\end{matrix}$

In equations (2) and (6), the voltage v_(M)=v_(inp)−v_(inn) is thedifferential input voltage. The voltage v_(Rn) will be induced onterminal w of CFOA3 (102 b) and will produce an inward current i_(Rn)through the parallel combination of R₂ and D₂ in series with the lowerpart of the potentiometer R₅. This current can be expressed as:

$\begin{matrix}{i_{R_{n}} = {\frac{- v_{R_{n}}}{R_{5{lower}} + R_{{eq}\; 2}}.}} & (7)\end{matrix}$

In equation (6) R_(5lower) is the resistance of the lower part of thepotentiometer R₅ and R_(eq2) is a nonlinear resistance that depends onthe status of the diode D₂. The voltage at terminal y of CFOA2 (102 c)can be expressed as:

$\begin{matrix}{v_{2} = {\frac{v_{R_{n}}\mspace{14mu} R_{5{lower}}}{R_{5{lower}} + R_{{eq}\; 2}}.}} & (8)\end{matrix}$

In equation (8), R_(5lower) is the resistance of the lower part of thepotentiometer R₅ and R_(eq2) is a nonlinear resistance that depends onthe status of the diode. This voltage will be induced on terminal x ofCFOA2 (102 c) and will be differentiated by the capacitor C₂. Thus, theinward current in the upper input terminal will be given by:

$\begin{matrix}{i_{inp} = {{- C_{2}}{\frac{\mathbb{d}v_{2}}{\mathbb{d}t}.}}} & (9)\end{matrix}$

Assuming that the diodes D₁ and D₂ are identical, C₁=C₃=C_(i),C₂=C₄=C_(d), R₂=R₃, and the potentiometer R₅ is midway with

${R_{5{upper}} = {R_{5{lower}} = {\frac{1}{2}R_{5}}}},$then R_(eq1)=R_(eq2)=R_(eq),

${v_{R_{n}} = {{- v_{R_{p}}} = {{- \frac{1}{2}}v_{R}}}},$i_(Rn)=i_(Rp)=i_(R) and v₂=−v₁. Combining equations (1) and (6), thevoltage v_(R)=v_(Rp)−v_(Rn) can be expressed as:

$\begin{matrix}{v_{R} = {{v_{R_{p}} - v_{R_{n}}} = {\frac{2}{C_{i}R_{1}}{\int{v_{m}{{\mathbb{d}t}.}}}}}} & (10)\end{matrix}$

Using equations (2), (3), (6) and (7) the current i_(R)=i_(Rp)=i_(Rn)can be expressed as:

$\begin{matrix}{i_{R} = {\frac{1}{k_{1}}{\int{v_{m}{{\mathbb{d}t}.}}}}} & (11)\end{matrix}$In equation (11) the parameter k₁ is given by,

$\begin{matrix}{k_{1} = {\frac{( {R_{5} + {2R_{eq}}} )C_{i}R_{1}}{2}.}} & (12)\end{matrix}$Also combining equations (5) and (9) the input current can be expressedas:

$\begin{matrix}{i_{M} = {i_{inp} = {i_{inn} = {k_{2}{\frac{\mathbb{d}v_{R}}{\mathbb{d}t}.}}}}} & (13)\end{matrix}$In equation (13) the parameter k₂ is given by:

$\begin{matrix}{k_{2} = {\frac{C_{d}R_{5}}{R_{5} + {2R_{eq}}}.}} & (14)\end{matrix}$

Equations (11) and (13) can be represented by models 200 a and 200 b ofFIGS. 2A and 2B, respectively. Models 200 a and 200 b correspond to avoltage-controlled memristor, where the voltage exciting the memristorv_(M) is integrated in the form of a current i_(R). This current isconverted via a nonlinear resistor to voltage v_(R), and the voltage istransformed by differentiation to the memristor current i_(M). As statedsupra, the present memristor emulator circuit uses four CFOAs. They areof type AD844. Simple Germanium (Ge) diodes in the circuit provide thenecessary nonlinear function. Four equal-valued, grounded capacitors (47nF) complete the z and x terminal connections for memristor circuit 100.Two equal-valued resistors (3 kΩ) complete the w and y terminalconnections for memristor circuit 100. The variability of the resistorconnections, wherein the equal-valued 3 kΩ resistors are interconnectedby a 1 kΩ potentiometer, allows for compensation for any mismatchbetween the capacitors (C₁, C₂, C₃, and C₄).

Experimental results of the floating memristor emulator circuit 100 areshown in plots 300 a, 300 b, 400 a, 400 b, and 500 of FIGS. 3A, 3B, 4A,4B, and 5, respectively. Inspection of the plots clearly shows thefrequency dependence of the memristance. As the frequency increases, thememristor emulator tends to behave as a normal resistor.

The functionality of the present floating memristor emulator circuit 100of FIG. 1 was tested by using it in FM-to-AM conversion. The FM-AMconversion circuit 600 shown in FIG. 6 is a simple frequency dependent,variable-gain inverting amplifier exploiting to advantage the frequencydependence of the memristance to form an FM discriminator circuit thatis used in the first stage of the FM demodulator 700 shown in FIG. 7.The FM-AM conversion circuit 600 was tested using an FM signal formed ofa carrier of frequency=2 kHz, a modulating frequency=100 Hz andfrequency deviation=900 Hz. As shown in FIG. 7, the output of FM-to-AMconverter (discriminator) 600 circuit of FIG. 6 was applied to anenvelope detector of the FM demodulator 700, which fully demodulates anFM signal input to the FM discriminator. A low pass filter follows theenvelope detector. The first stage of the FM demodulator uses thefloating memristor emulator 100 connected to the negative input of anoperational amplifier OA1 with resistive negative feedback (R1). Thepositive input of OA1 is connected to ground. Operational amplifierOA1's output feeds a second stage (envelope detector) of the FMdemodulator. The results obtained are shown in plots 800-1000 of FIGS.8-10, respectively. Inspection of plots 800 through 1000 clearly showsthat the present FM-to-AM converter works as expected and exploits toadvantage the frequency dependence of the floating memristor emulator100 of FIG. 1.

It is to be understood that the present invention is not limited to theembodiments described above, but encompasses any and all embodimentswithin the scope of the following claims.

We claim:
 1. A floating memristor emulator, comprising: first, second,third, and fourth current feedback operational amplifiers (CFOAs), eachof the CFOAs having y, x, z, and w terminals, the y terminal of thefirst CFOA being connected to the z terminal of the second CFOA, the yterminal of the third CFOA being connected to the z terminal of thefourth CFOA, and the x terminals of the first and third CFOAs being inoperable communication with each other; grounded capacitors C₁ and C₃connected to the respective z terminal of CFOAs one and three; groundedcapacitors C₂ and C₄ connected to the respective x terminal of CFOAs twoand four; a differential voltage input, v_(inp), v_(inn) formed from they terminals of the first and third CFOAs; a potentiometer R₅ havingfirst and second end terminals and a wiper, the first terminal beingconnected to the y terminal of the fourth CFOA, the second terminalbeing connected to the y terminal of the second CFOA, and the wiperbeing connected to ground; a first parallel resistor-diode combinationR₃ and D₁ connected in series with the first terminal of thepotentiometer R₅ and having a cathode portion of the diode D₁ connectedto the w terminal of the first CFOA; and a second parallelresistor-diode combination R₂ and D₂ connected in series with the secondterminal of the potentiometer R₅ and having an anode portion of thediode D₂ connected to the w terminal of the third CFOA.
 2. The floatingmemristor emulator according to claim 1, further comprising apotentiometer R₁ connected between the x terminals of the first andthird CFOAs to define the operable communication between the xterminals, the wiper of potentiometer R₁ being connected to the thirdCFOA.
 3. The floating memristor emulator according to claim 2, whereincurrent through the potentiometer R₁ is characterized by the relation:i _(R) ₁ =(v _(inp) −v _(inn))/R ₁, where v_(inp) is an input voltage atthey terminal of the first CFOA and v_(inn) is an input voltage at the yterminal of the third CFOA.
 4. The floating memristor emulator accordingto claim 3, wherein voltage at the w terminal of the first CFOA ischaracterized by the relation:$v_{R_{p}} = {\frac{1}{C_{1}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{\mathbb{d}t}.}}}}$5. The floating memristor emulator according to claim 4, wherein currentat the w terminal of the first CFOA is characterized by the relation:${i_{R_{p}} = \frac{v_{R_{p}}}{R_{5{upper}} + R_{{eq}\; 1}}},$ whereR_(5upper) is the first terminal of potentiometer R₅, and R_(eq1) is anonlinear equivalent resistance depending on the status of the diode D₁.6. The floating memristor emulator according to claim 5, wherein thevoltage v₁ at terminal y of the fourth CFOA is characterized by therelation:$v_{1} = {\frac{v_{R_{p}}R_{5{upper}}}{R_{5{upper}} + R_{{eq}\; 1}}.}$7. The floating memristor emulator according to claim 6, wherein anoutward current i_(inn) from the y terminal of the third CFOA ischaracterized by the relation:$i_{inn} = {C_{4}{\frac{\mathbb{d}v_{1}}{\mathbb{d}t}.}}$
 8. Thefloating memristor emulator according to claim 7, wherein a voltagev_(R) _(n) at the w terminal of the third CFOA is characterized by therelation:$v_{R_{n}} = {\frac{- 1}{C_{3}}{\int{\frac{v_{inp} - v_{inn}}{R_{1}}{{\mathbb{d}t}.}}}}$9. The floating memristor emulator according to claim 8, wherein currenti_(R) _(n) at the w terminal of the third CFOA is characterized by therelation:${i_{R_{n}} = \frac{- v_{R_{n}}}{R_{5{lower}} + R_{{eq}\; 2}}},$ whereR_(5lower) is the second terminal of potentiometer R₅, and R_(eq2) is anonlinear equivalent resistance depending on the status of the diode D₂.10. The floating memristor emulator according to claim 9, wherein thevoltage v₂ at terminal y of the second CFOA is characterized by therelation:$v_{2} = {\frac{v_{R_{n}}R_{5{lower}}}{R_{5{lower}} + R_{{eq}\; 2}}.}$11. The floating memristor emulator according to claim 10, wherein aninward current i_(inp) on the y terminal of the first CFOA ischaracterized by the relation:$i_{inp} = {{- C_{2}}{\frac{\mathbb{d}v_{2}}{\mathbb{d}t}.}}$
 12. Thefloating memristor emulator according to claim 11, wherein: diodes D₁and D₂ have identical value; an input capacitance C_(i) is characterizedby the relation C₁=C₃; an output capacitance C_(d) is characterized bythe relation C₂=C₄; the wiper of potentiometer is set midway with${R_{5{lower}} = {R_{5{lower}} = {\frac{1}{2}R_{5}}}};$ and adifferential voltage v_(R) from the w terminals of the first and thirdCFOAs is characterized by the relation:${v_{R} = {{v_{R_{p}} - v_{R_{n}}} = {\frac{2}{C_{i}R_{1}}{\int{v_{M}{\mathbb{d}t}}}}}},$where v_(M) is a differential input voltage characterized by therelation v_(inp)−v_(inn).
 13. The floating memristor emulator accordingto claim 12, wherein a differential current i_(R)=i_(Rp)=−i_(Rn) ischaracterized by the relation:${i_{R} = {\frac{1}{k_{1}}{\int{v_{M}{\mathbb{d}t}}}}},$ where k₁ is aparameter characterized by the relation:$k_{1} = {\frac{( {R_{5} + {2R_{eq}}} )C_{i}R_{1}}{2}.}$ 14.The floating memristor emulator according to claim 13, wherein adifferential input current i_(M) is characterized by the relation:${i_{M} = {i_{inp} = {i_{inn} = {k_{2}\frac{\mathbb{d}v_{R}}{\mathbb{d}t}}}}},$where k₂ is a parameter characterized by the relation:$k_{2} = {\frac{C_{d}R_{5}}{R_{5} + {2R_{{eq}\;}}}.}$
 15. The floatingmemristor emulator according to claim 14, further comprising: aninverting amplifier having an input and an output, the input beingconnected in a circuit with the floating memristor emulator, and whereingain of the output varies in relation to a frequency of a signal at theinput, defining an inverting amplifier-floating memristor circuitfunctioning as an FM discriminator.
 16. The floating memristor emulatoraccording to claim 15, further comprising an AM envelope detector havingan input and an output, the FM discriminator having an output connectedto the input of an AM envelope detector, the envelope detector having anoutput fully demodulating an FM signal input to the FM discriminator.